Thermoelectric effects in magnetic tunnel junctions are promising to serve as the basis for logic devices or memories in a ”green” information technology. However, up to now the readout contrast achieved with Seebeck effects was magnitudes smaller compared to the well-established tunnel magnetoresistance effect. Here, we resolve this problem by demonstrating that the tunnel magneto-Seebeck effect (TMS) in CoFeB/MgO/CoFeB tunnel junctions can be switched on to a logic “1” state and off to “0” by simply changing the magnetic state of the CoFeB electrodes. This new functionality is achieved by combining a thermal gradient and an electric field. Our results show that the signal crosses zero and can be adjusted by tuning a bias voltage that is applied between the electrodes of the junction; hence, the name of the effect is bias-enhanced tunnel magneto-Seebeck effect (bTMS). Via the spin- and energy-dependent transmission of electrons in the junction, the bTMS effect can be configured using the bias voltage with much higher control than the tunnel magnetoresistance and even completely suppressed for only one magnetic configuration. Moreover, our measurements are a step towards the experimental realization of high TMS ratios without additional bias voltage, which are predicted for specific Co-Fe compositions.